A302938 Lexicographically first sequence of distinct terms such that the sum of any two terms is not a term of the sequence, and the sum of any two digits is not a digit of the sequence.

1, 2, 4, 7, 44, 47, 74, 77, 444, 447, 474, 477, 744, 747, 774, 777, 4444, 4447, 4474, 4477, 4744, 4747, 4774, 4777, 7444, 7447, 7474, 7477, 7744, 7747, 7774, 7777, 44444, 44447, 44474, 44477, 44744, 44747, 44774, 44777, 47444, 47447, 47474, 47477, 47744, 47747, 47774, 47777, 74444, 74447

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Apr 16 2018

Keywords

• nonn
• base

Comments

The full sequence uses digits 4 and 7 only, except for a(1) = 1 and a(2) = 2.

Examples

			1 + 2 = 3 and there is no term or digit 3 in the sequence;
1 + 4 = 5 and there is no term or digit 5 in the sequence;
1 + 7 = 8 and there is no term or digit 8 in the sequence;
2 + 4 = 6 and there is no term or digit 6 in the sequence;
2 + 7 = 9 and there is no term or digit 9 in the sequence;
4 + 4 = 8 and there is no term or digit 8 in the sequence;
4 + 7 = 11 and there is no term 11 in the sequence;
7 + 7 = 14 and there is no term 14 in the sequence;
etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A302940 where the word “sum” is replaced by “product”.

Cf. A014261 which shares the same property (numbers that contain odd digits only).

Cf. A284971.

Formula

a(n) = A284971(n-2) for n>=3. - Alois P. Heinz, Jul 15 2023